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At least 613 records · Page 34Linked to original sources

arXiv1999

Interplay between Coherence and Incoherence in Multi-Soliton Complexes

We analyze photo-refractive incoherent soliton beams and their interactions in Kerr-like nonlinear media. The field in each of M incoherently interacting components is calculated using an integrable set of coupled nonlinear Schrodinger equations. In particular, we obtain a general N-soliton solution, describing propagation of multi-soliton complexes and their collisions. The analysis shows that the evolution of such higher-order soliton beams is determined by coherent and incoherent contributions from fundamental solitons. Common features and differences between these internal interactions are revealed and illustrated by numerical examples.

patt-sol↗

arXiv1999

Quasiperiodic Envelope Solitons

We analyse nonlinear wave propagation and cascaded self-focusing due to second-harmonic generation in Fibbonacci optical superlattices and introduce a novel concept of nonlinear physics, the quasiperiodic soliton, which describes spatially localized self-trapping of a quasiperiodic wave. We point out a link between the quasiperiodic soliton and partially incoherent spatial solitary waves recently generated experimentally.

patt-sol↗

arXiv1999

Hydrodynamics of the Kuramoto-Sivashinsky Equation in Two Dimensions

The large scale properties of spatiotemporal chaos in the 2d Kuramoto-Sivashinsky equation are studied using an explicit coarse graining scheme. A set of intermediate equations are obtained. They describe interactions between the small scale (e.g., cellular) structures and the hydrodynamic degrees of freedom. Possible forms of the effective large scale hydrodynamics are constructed and examined. Although a number of different universality classes are allowed by symmetry, numerical results support the simplest scenario, that being the KPZ universality class.

cond-mat.soft↗

arXiv1998

Patterns from preheating

The formation of regular patterns is a well-known phenomenon in condensed matter physics. Systems that exhibit pattern formation are typically driven and dissipative with pattern formation occurring in the weakly non-linear regime and sometimes even in more strongly non-linear regions of parameter space. In the early universe, parametric resonance can drive explosive particle production called preheating. The fields that are populated then decay quantum mechanically if their particles are unstable. Thus, during preheating, a driven-dissipative system exists. In this paper, we show that a self-coupled inflaton oscillating in its potential at the end of inflation can exhibit pattern formation.

hep-ph↗

arXiv1999

Quasi-Solitons in Dissipative Systems and Exactly Solvable Lattice Models

A system of first-order differential-difference equations with time lag describes the formation of density waves, called as quasi-solitons for dissipative systems in this paper. For co-moving density waves, the system reduces to some exactly solvable lattice models. We construct a shock-wave solution as well as one-quasi-soliton solution, and argue that there are pseudo-conserved quantities which characterize the formation of the co-moving waves. The simplest non-trivial one is given to discuss the presence of a cascade phenomena in relaxation process toward the pattern formation.

patt-sol↗

arXiv1999

On-off Intermittency in Stochastically Driven Electrohydrodynamic Convection in Nematics

We report on-off intermittency in electroconvection of nematic liquid crystals driven by a dichotomous stochastic electric voltage. With increasing voltage amplitude we observe laminar phases of undistorted director state interrupted by shorter bursts of spatially regular stripes. Near a critical value of the amplitude the distribution of the duration of laminar phases is governed over several decades by a power law with exponent -3/2. The experimental findings agree with simulations of the linearized electrohydrodynamic equations near the sample stability threshold.

patt-sol↗

arXiv1999

Tiling the plane without supersymmetry

We present a way of tiling the plane with a regular hexagonal network of defects. The network is stable and follows in consequence of the three-junctions that appear in a model of two real scalar fields that presents $Z_3$ symmetry. The $Z_3$ symmetry is effective in both the vacuum and defect sectors, and no supersymmetry is required to build the network.

hep-th↗

arXiv1999

Twirling and Whirling: Viscous Dynamics of Rotating Elastica

Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by a novel pair of coupled PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist/bend coupling and reveal two dynamical regimes separated by a Hopf bifurcation: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. The consequences of these phenomena for self-propulsion are investigated, and experimental tests proposed.

cond-mat.soft↗

arXiv1999

Impurity-induced stabilization of solitons in arrays of parametrically driven nonlinear oscillators

Chains of parametrically driven, damped pendula are known to support soliton-like clusters of in-phase motion which become unstable and seed spatiotemporal chaos for sufficiently large driving amplitudes. We show that the pinning of the soliton on a "long" impurity (a longer pendulum) expands dramatically its stability region whereas "short" defects simply repel solitons producing effective partition of the chain. We also show that defects may spontaneously nucleate solitons.

patt-sol↗

arXiv1999

Influence of four-wave mixing and walk-off on the self-focusing of coupled waves

Four-wave mixing and walk-off between two optical beams are investigated for fo cusing Kerr media. It is shown that four-wave mixing reinforces the self-focusi ng of mutually-trapped waves by lowering their power threshold for collapse, on ly when their phase mismatch is small. On the contrary, walk-off inhibits the c ollapse by detrapping the beams, whose partial centroids experience nonlinear o scillations.

patt-sol↗

arXiv1999

Statistical mechanics of a nonlinear discrete system

Statistical mechanics of the discrete nonlinear Schrödinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of $T=\infty$, we identify a phase transition, through a discontinuity in the partition function. The phase transition is demonstrated to manifest itself in the creation of breather-like localized excitations. Interrelation between the statistical mechanics and the nonlinear dynamics of the system is explored numerically in both regimes.

cond-mat.stat-mech↗

arXiv1999

Defect Chaos of Oscillating Hexagons in Rotating Convection

Using coupled Ginzburg-Landau equations, the dynamics of hexagonal patterns with broken chiral symmetry are investigated, as they appear in rotating non-Boussinesq or surface-tension-driven convection. We find that close to the secondary Hopf bifurcation to oscillating hexagons the dynamics are well described by a single complex Ginzburg-Landau equation (CGLE) coupled to the phases of the hexagonal pattern. At the bandcenter these equations reduce to the usual CGLE and the system exhibits defect chaos. Away from the bandcenter a transition to a frozen vortex state is found.

patt-sol↗

arXiv1999

Pattern formation in inclined layer convection

We report experiments on thermally driven convection in an inclined layer of large aspect ratio in a fluid of Prandtl number $σ\approx 1$. We observed a number of new nonlinear, mostly spatio-temporally chaotic, states. At small angles of inclination we found longitudinal rolls, subharmonic oscillations, Busse oscillations, undulation chaos, and crawling rolls. At larger angles, in the vicinity of the transition from buoyancy- to shear-driven instability, we observed drifting transverse rolls, localized bursts, and drifting bimodals. For angles past vertical, when heated from above, we found drifting transverse rolls and switching diamond panes.

patt-sol↗

arXiv1999

Discrete stochastic modeling of calcium channel dynamics

We propose a simple discrete stochastic model for calcium dynamics in living cells. Specifically, the calcium concentration distribution is assumed to give rise to a set of probabilities for the opening/closing of channels which release calcium thereby changing those probabilities. We study this model in one dimension, analytically in the mean-field limit of large number of channels per site N, and numerically for small N. As the number of channels per site is increased, the transition from a non-propagating region of activity to a propagating one changes in nature from one described by directed percolation to that of deterministic depinning in a spatially discrete system. Also, for a small number of channels a propagating calcium wave can leave behind a novel fluctuation-driven state, in a parameter range where the limiting deterministic model exhibits only single pulse propagation.

patt-sol↗

arXiv1999

Anomalous resonance phenomena of solitary waves with internal modes

We investigate the non-parametric, pure ac driven dynamics of nonlinear Klein-Gordon solitary waves having an internal mode of frequency $Ω_i$. We show that the strongest resonance arises when the driving frequency $δ=Ω_i/2$, whereas when $δ=Ω_i$ the resonance is weaker, disappearing for nonzero damping. At resonance, the dynamics of the kink center of mass becomes chaotic. As we identify the resonance mechanism as an {\em indirect} coupling to the internal mode due to its symmetry, we expect similar results for other systems.

cond-mat.stat-mech↗

arXiv1999

Time resolved pattern evolution in a large aperture laser

We have measured quasi-instantaneous transverse patterns in a broad aperture laser. Non-ordered patterns yielding to boundary determined regular structures in progressive time-integrated recording are observed. The linear analysis and numerical integration of the full Maxwell-Bloch equations allow us to interpret the features of the experiment. We show that this system being far from threshold cannot be fully understood with a perturbative model.

patt-sol↗

arXiv2000

Interface and contact line motion in a two phase fluid under shear flow

A coarse grained description of a two phase fluid is used to study the steady state configuration of the interface separating the coexisting phases, and the motion of the contact line at which the interface intersects a solid boundary. The fluid is set in motion by displacing two parallel, infinite solid boundaries along their own plane. Dissipative relaxation of the order parameter leads to interfacial slip at the contact line, even when no-slip boundary conditions for the fluid velocity are considered. This relaxation occurs within a characteristic length scale l that depends on the order parameter mobility, the equilibrium interfacial tension, the imposed wall velocity, the thermal correlation length, the equilibrium miscibility gap, and the mutual diffusion coefficient. Steady-state interface equations which describe the system on a length scale large compared to the correlation length are derived. Scaling forms which involve the ratio l/L, where L is the width of the fluid layer, and the capillary number follow from the interface equations. The scaling results are verified by direct numerical solution of the governing equations.

cond-mat.stat-mech↗

arXiv2000

Dynamics of localized structures in vector waves

Dynamical properties of topological defects in a twodimensional complex vector field are considered. These objects naturally arise in the study of polarized transverse light waves. Dynamics is modeled by a Vector Complex Ginzburg-Landau Equation with parameter values appropriate for linearly polarized laser emission. Creation and annihilation processes, and selforganization of defects in lattice structures, are described. We find "glassy" configurations dominated by vectorial defects and a melting process associated to topological-charge unbinding.

patt-sol↗